Map Projection Overview
I made six different world maps showing Washington, DC and Baghdad, Iraq, using six different map projections. I chose to use six different cylindrical projections, two of which are conformal, two of which are equal area, and two of which are equal distance. The two conformal map projections are the Mercator and Miller Cylindrical Projections. The two equal area projections are the Equal Area Cylindrical and Behrmann Projections. The two equal distance projections are the Equal Distance Cylindrical and Plate Carree Projections. All six map projections exhibit considerable distortion in various ways.
The Mercator and Miller Cylindrical Projections are conformal map projections because they preserve the correct angles of map objects. It is thus easily possible to draw rhumb lines (lines that cross meridians), greatly helping with sea navigation, the original purpose of the Mercator Projection. The Mercator Projection does have considerable land area distortion, especially with increasing distance from the Equator. For example, Alaska, Canada, Greenland, and Russia appear much larger than they really are, and Antarctica is enormous, because the distance between parallels increases as the distance from the equator increases. The Miller Cylindrical Projection is an attempt to improve the Mercator Projection, by scaling the parallels of latitude by 2/5, and then multiplying them by 5/4 at the Equator to minimize distortion. Thus, the Miller Cylindrical Projection is not truly conformal, because the angles change slightly, but it is descended from the conformal Mercator Projection, and is very similar. Thus, the Miller Cylindrical Projection also exhibits many of the same distortions. The distance between parallels still increases as distance from the equator increases. Alaska, Canada, Greenland, and Russia are still larger than they really are, although not as large as in the Mercator Projection; the Miller Cylindrical Projection also shows more of the northern extremes of Earth. However, Antarctica is truly monstrous; it was already too big in the Mercator Projection, and it looks twice as large in the Miller Cylindrical Projection. For both projections, long range distance distortion is also a problem; Baghdad is essentially the same distance away from Washington, DC on both projections (8,415 miles and 8,413 miles, respectively), when Baghdad is actually 6,208 miles away from Washington, according to travelmath.com (which measures air miles and uses the great circle formula). Thus, there is plenty of distortion on cylindrical conformal projections. Yet the cylindrical equal area projections did not demonstrate to be any better.
The Equal Area Cylindrical and Behrmann Projections are equal area projections because they preserve the actual area of the countries depicted, so the countries remain correct in size. The distance between parallels decreases as distance from the equator increases, so Alaska, Canada, Greenland, Russia, and Antarctica seem compacted against the top and bottom edges of the projections. Still, on both projections, Alaska, Canada, Greenland, and Russia appear to be the correct size, while Antarctica is still too big, though not as big as on the conformal projections. Long range distance distortion is still a problem for both projections; Baghdad is 8,407 miles away from Washington on the Equal Area Cylindrical Projection, and 7,288 miles away on the Behrmann Projection. The Behrmann Projection shows the most improvement in reducing distortion in general.
Finally, the Equal Distance Cylindrical and Plate Carree Projections are equal distance projections because they maintain a consistent distance between all parallels and meridians. Thus, there seems to be less distortion in terms of geographic coordinates, even though there is extensive distortion in other areas. Far northern landmasses are larger than they should be, like with the conformal cylindrical projections, and Antarctica is still very large, like with the conformal and equal area cylindrical projections. Long range distance distortion is significant, like with the conformal projections. For instance, on the Plate Carree Projection, Baghdad is 8,415 miles away from Washington, which is basically the same distance measured on the Mercator, Miller Cylindrical, and Equal Area Cylindrical Projections. Notably, on the Equal Distance Cylindrical Projection, Baghdad is only 4,218 miles away from Washington, or about half the distance measured on the other projections, and well short of the actual 6,208 air miles between Washington and Baghdad. The Equal Distance Cylindrical Projection seems compacted horizontally, or taller and thinner than most maps, because there appears to be a relatively small distance between meridians, and a relatively large distance between parallels. Conversely, the Plate Carree Projection maintains the same distance between parallels as between meridians, so that the latitude-longitude grid consists of squares, rather than rectangles. The result is generally more balance to the shapes of and distances between landforms.
I chose to create six world maps with cylindrical projections because I think their rectangular shapes look nice on rectangular websites and sheets of paper. Yet all the cylindrical projections show distortions in terms of size, shape, and distance, some worse than others. Overall, the Behrmann Projection shows the least distortion of any of the cylindrical projections I examined. Because it is an equal area projection, all the countries and landmasses except for Antarctica have the correct size. Shape is also mostly correct, except for Antarctica, while the northern areas do look somewhat compacted. There is also less long range distance distortion on the Behrmann Projection, compared to all the other cylindrical projections; Baghdad is 7,288 miles away from Washington on the Behrmann world map, and 6,208 miles away on a globe.
1) An ellipsoid is an irregular, imperfect sphere. It is a mathematical surface defined by revolving an ellipse around its minor (polar) axis. It approximates the surface of the Earth without topographic undulations. On a two dimensional service, Earth is an ellipsoid.
2) Earth's imaginary network of intersecting lines of latitude and longitude is the graticule, and is a representation of a coordinate system.
3) Magnetic North is where a compass points, while the North Pole is one of the poles of Earth's axis of rotation.
4) A datum is a three dimensional frame of reference (model of the earth) used to determine surface locations, defining the origin and orientation of latitude and longitude. A datum consists of a specified ellipsoid and a set of surveyed coordinate locations specifying horizontal positions for a horizontal datum or vertical positions for a vertical datum on the surface of the Earth. Cartographers develop datums through surveys and monument points.
5) A map projection is a transformation of coordinate locations from the curved surface of the Earth onto flat maps.
6) A developable surface is a surface without distortion when flattened on a plane.
7) Lines of longitude run north-south on the graticule, converge on the poles, and mark angular distance east and west of the prime meridian.
8) The GRS80 ellipsoid is the best model of the Earth for North America, especially as the foundation for the North American Datum of 1983.
9) The Universal Transverse Mercator global coordinate system would be appropriate to use for developing and analyzing spatial data when mapping countries or larger areas, because there is minimal distortion within its mapped segments, which all have an equal width of 60 degrees of longitude .
10) Great circle distance is the shortest distance between any two points on the surface of a sphere.
